Question

What is the perimeter of a triangle with corners at `(3 ,6 )`, `(1 ,5 )`, and `(8 ,1 )`?

Answer 1

Perimeter, `P =bar(AB)+bar(BC)+bar(CA)= sqrt(5)+sqrt(65)+5sqrt(2)`

Explanation:

Use the distance formula to determine: `bar(AB), bar(BC), bar(CA)`
The Distance Formula between 2 points:
`P_1(x_1, y_1)`, `P_2(x_2, y_2)`
`bar(P_1P_2) = sqt((x_2-x_1 )^2 + (y_2-y_1 )^2)` so then
`bar(AB) = sqrt((3-1)^2+(6-5)^2)=sqrt(5)`
`bar(BC) = sqrt((1-8)^2+(5-1)^2)=sqrt(65)`
`bar(CA) = sqrt((8-3)^2+(1-6)^2)=5sqrt(2)`
Perimeter, `P =bar(AB)+bar(BC)+bar(CA)= sqrt(5)+sqrt(65)+5sqrt(2)`